Final answer:
To find the derivative f'(3), given functions u(t) and v(t) with certain values at t=3, we need to use the product rule for differentiation. However, the question has typos, thus the precise values of u(3) and u'(3) are unclear, and further clarification is needed to provide the exact value of f'(3).
Step-by-step explanation:
To find f'(3), where f(t) = u(t) · v(t), and given u(3), u'(3), and v(t), we need to use the product rule for differentiation, which states that (f · g)' = f' · g + f · g'. The functions u(t) and v(t) are not specified but we have the values at t = 3. Assuming the typo '1, 2, -1' represents the three possible values for u(3) and '8, 1, 4' represents the possible values for u'(3), we can find f'(3) for each combination by differentiating v(t) accordingly.
We also have v(t) = t, t², t³ which implies we need to differentiate each of these to find v'(t). Hence, we need to find the instantaneous velocity and then evaluate at t = 3 using the appropriate product of the derivatives of u(t) and v(t) at 3.
Unfortunately, the question contains typographical errors and it's unclear which combinations of u(3) and u'(3) should be used with the different forms of v(t). Assuming the intended question is to apply the given u(3) and u'(3) with each form of v(t), we'd use the product rule for each case. The complete solution would require further clarification from the student.